We study the role of the dipolar-induced resonance (DIR) in a quasi-one-dimensional system of ultracold bosons. We first describe the effect of the DIR on two particles in a harmonic trap. Then, we consider a deep optical lattice loaded with ultracold dipolar bosons. In order to describe this system, we introduce a novel atom-dimer extended Bose-Hubbard model, which is the minimal model correctly accounting for the DIR. We analyze the impact of the DIR on the phase diagram at T=0 by exact diagonalization of a small-sized system. We show that the DIR strongly affects this phase diagram. In particular, we predict the mass density wave to occur in a narrow domain corresponding to weak nearest-neighbor interactions, and we predict the occurrence of a collapse phase for stronger dipolar interactions.