We estimate the dipole of the whole-sky, X-ray flux-limited sample of Abell/Abell, Corwin, & Olowin (ACO) clusters (XBACs) and compare it to the optical cluster dipole, which is known to be well aligned with the cosmic microwave background (CMB) dipole and which converges to its final value at ~160 h-1 Mpc. We find the X-ray cluster dipole to be well aligned (<~25°) with the CMB dipole, while it closely follows the radial profile of its optical cluster counterpart, although its amplitude is about 10%-30% lower. In view of the fact that the XBAC sample is not affected by the volume incompleteness and the projection effects that are known to exist at some level in the optical parent Abell/ACO cluster catalog, our present results confirm the previous optical cluster dipole analysis that there are significant contributions to the Local Group motion from large distances (~160 h-1 Mpc). In order to assess the expected contribution to the X-ray cluster dipole from a sample that is closer to being purely X-ray-selected, we compare the dipoles of the XBACs and the brightest-cluster sample in their overlap region. The resulting dipoles are in good mutual agreement with an indication that the XBAC sample slightly underestimates the full X-ray dipole (by <~5%), while the Virgo Cluster contributes about 12% to the overall X-ray cluster dipole. Using linear perturbation theory to relate the X-ray cluster dipole to the Local Group peculiar velocity, we estimate βcX (≡Ω0.60/bcX)~=0.24+/-0.05.