The staggering range and sheer excellence of John Dominis’ pictures — his Korean War coverage; his portraits of pop-culture icons like Sinatra, Redford and McQueen; his beautiful treatment of the “big cats” of Africa; his virile sports photography — place him firmly among the premier photojournalists of the last 75 years. But a lesser-known photo essay that Dominis shot for LIFE magazine, focusing on the plight of Appalachia in the early 1960s, spotlights another aspect of the man’s great talent: namely, an ability to portray the forgotten and the afflicted while, miraculously, conveying both the ragged dignity of his subjects, and the furious indignation smoldering in the heart behind the camera.

The piece in which Dominis’ photos appeared — an extraordinary 12-page feature in the Jan. 31, 1964, issue of LIFE, titled “The Valley of Poverty” — was one of the very first substantive reports in any American publication on President Lyndon Johnson’s nascent “war on poverty.” At the time, LIFE was arguably the most influential weekly magazine in the country, and without doubt the most widely read magazine anywhere to regularly publish major photo essays by the world’s best photographers. That said, LIFE was in a unique position in the early days of Johnson’s administration to not merely tell but to show its readers what was at stake, and what the challenges were, as the new president’s “Great Society” initiatives got under way.

“The Valley of Poverty,” illustrated with some of the most powerful and, at the same time, some of the most intimate photographs of John Dominis’ extraordinary career, served (and still serves today) as an indictment of a wealthy nation’s indifference, and a plea — if not a demand — that the rest of the country not turn its back on the suffering of so many of its least powerful citizens.

As LIFE put it to the magazine’s readers in January 1964:

In a lonely valley in eastern Kentucky, in the heart of the mountainous region called Appalachia, live an impoverished people whose plight has long been ignored by affluent  America. Their homes are shacks without plumbing or sanitation. Their landscape is a man-made desolation of corrugated hills and hollows laced with polluted streams. The people, themselves — often disease-ridden and unschooled — are without jobs and even without hope. Government relief and handouts of surplus food have sustained them on a bare subsistence level for so many years that idleness and relief are now their accepted way of life.

President Johnson, who has declared “unconditional war on poverty in America,” has singled out Appalachia as a major target… Appalachia stretches from northern Alabama to southern Pennsylvania, and the same disaster that struck eastern Kentucky hit the whole region — the collapse of the coal industry 20 years ago, which left Appalachia a vast junkyard. It was no use for the jobless miners to try farming — strip mining has wrecked much of the land and, in any case, the miners had lost contact with the soil generations ago… Unless the grim chain [of unemployment and lack of education] can be broken, a second generation coming of age in Appalachia will fall into the same dismal life — a life that protects them from starvation but deprives them of self-respect and hope.