Can anything of significant mass travel faster than the speed of light?

We all know that Einstein stated that nothing can travel faster than the speed of light, because of its mass. But say this was the situation; I am traveling at the speed of light. In my hand, I have a stone. I attempt to throw this stone forwards, in the direction in which I am traveling. Doesn't the speed of the stone from the force I exerted onto it with my arm ADD to the speed at which it was already traveling at (which in my hand, before it was thrown, was traveling at the speed of light) THEREFORE allowing the stone travel FASTER than the speed of light?