Sweet Smell of Success Question

I won’t bother to explain the situation in which a character says the line in which I have a question about, since I am quite sure that many dopers are very familiar with the movie and need no explanation. With that said, J.J. Hunsecker says the following: “My left hand hasn’t seen my right hand in twenty years.” My question is, what the hell is he talking about, or, in other words, what does the line in question mean?

You don’t need to know the movie or play to get it.

Think of the phrase, “His left hand doesn’t know what his right hand is doing.” This is just a humorous extrapolation.