Here's a nice graph from the us census bureau. At the surface level, it seems like young people were more likely to vote during the 60s, but there's a few important considerations here:

1. Voter turnout was higher, then declined for every group except those over 65.

2. The 26th Amendment (lowering the voting age to 18) was not passed until 1971, so the line on this graph before that is actually 21-24 year olds.

3. The draft for the Vietnam war ended in 1973, removing what had been a key political motivation for younger voters.