Along with trade comes aspects of culture like seals and working techniques. Right now the prevailing sentiment of historians is that we're not 100% sure. We know there was trade exchange of course, and we have burial evidence of citizens being cross-buried which indicates travel between the two societies. The only definite answer I can give is that we don't know right now. Jonathan Mark Kenoyer, the leading expert on the Indus Valley, has observed trade and human movement between the Indus Valley, Oman as well as Mesopotamia. We just don't know to what extent culture was shared since we don't have much textual evidence.

See: Journal of Archaeological Science Volume 40, Issue 5, May 2013, Pages 2286–2297