Suppose I have a reversible reaction and the forward reaction is endothermic. Now if I increase the temperature, the rate of the forward reaction will increase but as I increase the temperature, the backward rate will simultaneously increase too as the average kinetic energies of the product molecules will be increasing, so the odds of successful collisions will be increased on the backward reaction too.

According to Le Chatelier's Principle, if I increase the temperature of a system (where the forward reaction is endothermic), equilibrium will be shifted to the right.

But isn't this wrong as the backward rate would increase too and the two increasing rates (forward and backward) would counteract each other and the equilibrium position would remain constant?