Replying to Traffic ticket

I got a ticket the other day on the way back from a concert. The ticket was for driving into the wrong lane, which was entirely because I drive a pretty big truck that can't safely take the tight turns that Poughkipsee, NY has to offer. I had to cross over the yellow line a bit, and first made sure there were no cars coming. But that doesn't matter. They said once I send in the "guilty" plea they will send me a fine in the mail. My question is, can I send in the payment for the fine with my "guilty" plea and have them take it? +K for actual answers, -K for hate or trolling. Thanks NSG.