Sounds like all you need is a mono to stereo adapter for your cord.
If the output on the cassette player is actually mono and the patch cord you have running to your AUX port is Stereo, then all you need is something like the the following:
Adapter
On the other hand, your cassette player may be stereo and your patch cord may be mono.. which, in case, I would purchase another cord.
Hope this helps.