Within the post-form distorted wave Born approximation wherein pure Coulomb, pure nuclear and their interference terms are treated consistently in a single setup we study the beam energy dependence of the Coulomb-nuclear interference terms in the breakup of $^{11}\mathrm{Be}$ on a medium mass $^{44}\mathrm{Ti}$ target. Our results suggest that the Coulomb-nuclear interference terms are dependent on the incident beam energy and can be as big as that of the individual Coulomb or nuclear terms depending on the angle and energy of the breakup fragments. We also calculate the relative energy spectra and one-neutron removal cross sections in the breakup of $^{11}\mathrm{Be}$ on a heavy $^{208}\mathrm{Pb}$ target at 69 MeV/nucleon for two different angular ranges of the projectile center of the mass scattering angle and compare them with recently available experimental data.