Slavery didn't export or transmit Roman culture as much as Roman citizens and traders settling conquered lands, and mixing with local elites, who adopted Roman traditions, economics, and lifestyles.
My reading of the history is that the literate Roman slaves more-or-less bought in to the system-- indeed, for the literate slave, there were paths to freedom, and some of the most trusted imperial advisers were freedmen. While slave uprisings were always a huge concern in Rome, they played no part in the eventual downfall of Rome, and the most remembered one-- Spartacus-- was of the illiterate war captive type of slave.
