The concept of a hybrid laser plasma accelerator is proposed. Relativistic electrons undergoing resonant betatron oscillations inside the plasma bubble created by a laser pulse are accelerated by gaining energy directly from the laser pulse and from its plasma wake. The resulting phase space of self-injected plasma electrons is split into two, containing a subpopulation that experiences wakefield acceleration beyond the standard dephasing limit because of the multidimensional nature of its motion that reduces the phase slippage between the electrons and the wake.