Measurements are presented by the CMS Collaboration at the Large Hadron Collider (LHC) of the higher-order harmonic coefficients that describe the azimuthal anisotropy of charged particles emitted in root s(NN) = 2.76 TeV PbPb collisions. Expressed in terms of the Fourier components of the azimuthal distribution, the n = 3-6 harmonic coefficients are presented for charged particles as a function of their transverse momentum (0.3 < p(T) < 8.0 GeV/c), collision centrality (0\%-70\%), and pseudorapidity (|eta| < 2.0). The data are analyzed using the event plane, multiparticle cumulant, and Lee-Yang zeros methods, which provide different sensitivities to initial-state fluctuations. Taken together with earlier LHC measurements of elliptic flow (n = 2), the results on higher-order harmonic coefficients develop a more complete picture of the collective motion in high-energy heavy-ion collisions and shed light on the properties of the produced medium.