Cooling of a 58 MHz micro-mechanical resonator from room temperature to 11 K is demonstrated using cavity enhanced radiation pressure. Detuned pumping of an optical resonance allows enhancement of the blue shifted motional sideband (caused by the oscillators Brownian motion) with respect to the red-shifted sideband leading to cooling of the mechanical oscillator mode. The reported cooling mechanism is a manifestation of the effect of radiation pressure induced dynamical backaction. These results constitute an important step towards achieving ground state cooling of a mechanical oscillator.