'The sixties' as envisioned by nostalgia don't even start until 1967. Before that everything is still very conservative. Early Beatles pop tunes, not Sgt. Pepper. They start fizzling out at the same time the Vietnam War does. Nixon explicitly ended the draft to end the antiwar movement, and without the unifying fear of being sent to die the youth protests disintegrated into a hundred crackpot sects.
US pulls out in 1975, Bicentennial return of patriotism is 1976, as well as the advent of the lumpenproletariat's version of liberation - disco, Star Wars is 1977, the first 'don't worry, be happy' premonition of the eighties.
So the sixties were 1967-1975.