The shear strength of dense granular flows is generally described by an effective friction coefficient, ratio of shear to normal stress, as a function of the inertial number I. However, this ratio depends on the normal stress when the particles interact via both friction and adhesion forces, and in this sense it does not properly represent a Coulomb-like friction. For the same reason, it is not a unique function of I. We used extensive contact dynamics simulations to isolate the cohesive strength from the purely frictional strength in dense inertial flows for a broad range of shear rates and adhesion forces between particles. Remarkably, while the frictional part of the strength increases with I, the cohesive strength is found to be a decreasing function of I. We show that a single dimensionless parameter, combining interparticle adhesion with I, controls not only the cohesive strength but also the packing fraction and granular texture in inertial flows.