Quoting from the Handbook of Current English-Seventh Edition (Corder and Ruszkiewicz):
"Nouns Referring to Individuals in a Group:
When a collective noun refers to the members of the group, especially if it represents them as acting individually, a plural verb and plural reference words are used:
The audience have taken their seats (emphasis mine)."
I'm going with minds as grammatically correct, although I like the "fix" listed above..."The only values that men can offer me are the works of their minds"
Rick