The second and the third order anisotropic flow, V2 and V3, are mostly determined by the corresponding initial spatial anisotropy coefficients, epsilon2 and epsilon3, in the initial density distribution. In addition to their dependence on the same order initial anisotropy coefficient, higher order anisotropic flow, Vn (n > 3), can also have a significant contribution from lower order initial anisotropy coefficients, which leads to mode-coupling effects. In this Letter we investigate the linear and non-linear modes in higher order anisotropic flow Vn for n = 4, 5, 6 with the ALICE detector at the Large Hadron Collider. The measurements are done for particles in the pseudorapidity range eta < 0.8 and the transverse momentum range 0.2 < pT < 5.0 GeV/c as a function of collision centrality. The results are compared with theoretical calculations and provide important constraints on the nature of the initial geometry fluctuations as well as the ratio of the shear viscosity to entropy density of the produced system.