AGN feedback is invoked as one of the most relevant mechanisms that shape the evolution of galaxies . Our goal is to understand the interplay between AGN feedback and the interstellar medium in M51 , a nearby spiral galaxy with a modest AGN and a kpc-scale radio jet expanding through the disc of the galaxy . For that purpose , we combine molecular gas observations in the CO ( 1-0 ) and HCN ( 1-0 ) lines from the Plateau de Bure interferometer with archival radio , X-ray , and optical data . We show that there is a significant scarcity of CO emission in the ionisation cone , while molecular gas emission tends to accumulate towards the edges of the cone . The distribution and kinematics of CO and HCN line emission reveal AGN feedback effects out to r \sim 500 pc , covering the whole extent of the radio jet , with complex kinematics in the molecular gas which displays strong local variations . We propose that this is the result of the almost coplanar jet pushing on molecular gas in different directions as it expands ; the effects are more pronounced in HCN than in CO emission , probably as the result of radiative shocks . Following previous interpretation of the redshifted molecular line in the central 5 ^ { \prime \prime } as caused by a molecular outflow , we estimate the outflow rates to be \dot { M } _ { \mathrm { H } _ { 2 } } \sim 0.9 M _ { \odot } / \mathrm { yr } and \dot { M } _ { \mathrm { dense } } \sim 0.6 M _ { \odot } / \mathrm { yr } , which are comparable to the molecular inflow rates ( \sim 1 M _ { \odot } / \mathrm { yr } ) ; gas inflow and AGN feedback could be mutually regulated processes . The agreement with findings in other nearby radio galaxies suggests that this is not an isolated case , and probably the paradigm of AGN feedback through radio jets , at least for galaxies hosting low-luminosity active nuclei .