As long as "play sounds" is enabled, under settings>board and pieces, you should be able to hear both. There is a similar post about this issue, along with a possible fix here:
https://www.chess.com/forum/view/help-support/no-sound-on-desktop-ok-on-apps-any-ideas
I can hear my own moves but not my opponents? Is there a settings for this or is it a bug ?