The student pilot stated that prior to departure for a solo cross-country flight, his flight instructor informed him he would notice extra aft weight when lifting off as this was the first time flying the helicopter solo with full fuel tanks. The student pilot stated that as the helicopter became light on its skids, he felt it tilt aft, and corrected with the application of cyclic and anti-torque pedals. As he raised the collective and lifted off the ground, the helicopter turned to the right, and he immediately lowered the collective and set the helicopter back down. The helicopter's tail skid “stinger” impacted the ground, and the helicopter sustained substantial damage to the vertical stabilizer. The student pilot stated there were no mechanical malfunctions or anomalies with the helicopter, and that the right turn may have been prevented by additional left anti-torque pedal application.