The way you described it sounds fine: "I acknowledge that we grew up in different cultures and that those cultures are probably pretty different." Trying to say anything else might be over-complicating it, imho.
But if you're looking for alternatives, you might say that you recognize your privilege.
I can't find an official reference for this specific term, but googling recognize privilege returns a ton of results showing its use.
This has a connotation that you're admitting that parts of your life might have been easier than parts of other lives, which may or may not be appropriate depending on your context.
You might also say that you've had a sheltered life:
protected from difficulties or unpleasant realities.
"she led a sheltered life until her mother and father went through a bitter divorce"
This carries the connotation that maybe you were a bit naive or unaware, which may or may not be correct for your context. Again, it's going to depend entirely on what you're trying to say.