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.