OK, since coming to this site years ago and learning a lot, I started using dumbells quite a bit (used to use machines primarily, whatever).
For whatever reason, my right side is just a tad stronger than my left (I'm right-handed, BTW). That is, whatever exercise I may do, if I go to failure I can squeeze out 1, maybe 2 more reps with my right arm. It doesn't bother me so much, but I'm just curious as to why I still have the imbalance after training for an extended period of time with dumbells and using the same amount of volume/intensity on each side.
Imbalances are going to be a normal part of the training routine (although you don't have to be hindered or limited by it).
Imbalances probably occurs from firing patterns of the neurons. Since you are right handed, it is likely that the patterns establish themselves more rapidly than your left side. Remember, muscle recruitment is established by firing patterns of neurons first (to utilize the existing muscles) before hypertrophy sets in.
It is reasonable to conclude that the neural patterns for the right side got set early on and hypertrophy occured much earlier than for the left side. While your right side was experiencing hypertrophy, your left side still needed time to lay in the firing pattern.
So, when the left side finally got to the point where it is growing from hypertrophy, the right side already had a couple more weeks of hypertrophy, making it that much stronger than the other side (yet, not enough so that one side is ridiculously stronger than the other). That's my take on the whole thing anyways.