No that kind of gain is not impossible. But I can tell you that you will need to eat like a fiend and train smart.
Since you're a beginner, I'd recommend lifting higher reps (8-12) per set for a few months. Then start gradually lowering back down to 6. Also, since you're a beginner, the volume is probably not going to kill you, but as you start lifting heavier weights, you might find that you may be overtraining with a workout like you've got now. Keep your current program for a month, and then try out some of the high quality routines on this site.
Training smart is at least as good as training hard! Oh, and eat a lot (see the Massive Eating article(s) by Dr. Berardi), drink a lot of water, and sleep a lot. At 5'11" and 126 you're unlikely to reach your goals... it'll be much better if you can gain some weight along the way.
One last piece of advice: Just because you have goals with bench, don't let the rest of your body lag. Believe it or not, a strong chest relies on a strong back, which in turn relies on strong legs. Don't short-change the other parts of your body.