The elliptic, v(2), triangular, v(3), and quadrangular, v(4), azimuthal anisotropic flow coefficients are measured for unidentified charged particles, pions, and (anti-)protons in Pb-Pb collisions at root S-NN = 2.76 TeV with the ALICE detector at the Large Hadron Collider. Results obtained with the event plane and four-particle cumulant methods are reported for the pseudo-rapidity range vertical bar eta vertical bar 8 GeV/c. The small p(T) dependence of the difference between elliptic flow results obtained from the event plane and four-particle cumulant methods suggests a common origin of flow fluctuations up to p(T) = 8 GeV/c. The magnitude of the (anti-)proton elliptic and triangular flow is larger than that of pions out to at least p(T) = 8 GeV/c indicating that the particle type dependence persists out to high p(T).