We report high-precision measurements of the deeply virtual Compton scattering (DVCS) cross section at high values of the Bjorken variable xB. DVCS is sensitive to the generalized parton distributions of the nucleon, which provide a three-dimensional description of its internal constituents. Using the exact analytic expression of the DVCS cross section for all possible polarization states of the initial and final electron and nucleon, and final state photon, we present the first experimental extraction of all four helicity-conserving Compton form factors (CFFs) of the nucleon as a function of xB, while systematically including helicity flip amplitudes. In particular, the high accuracy of the present data demonstrates sensitivity to some very poorly known CFFs.