Over the past 20 years, fullerides have been studied as the source of high-transition-temperature (T-c) superconductivity except for copper oxides. The recent finding of the Mott insulating state right beside superconductivity in Cs3C60 has suggested that magnetism helps raise T-c even in fullerides as in heavy-fermion compounds, high-T-c copper oxides, two-dimensional organic conductors, and iron pnictides. Namely, one tends to think that the link between Mott insulator and superconductivity takes place in fullerides, which can give rise to the mechanism beyond the Bardeen-Cooper-Schrieffer framework. However, the relationship between the Mott state and the superconductivity in Cs3C60 is still under debate. By nuclear magnetic resonance measurements under pressure, we find that the magnetism and superconductivity in Cs3C60 are competing orders. Different from previous reports, the phase separation of Cs3C60 crystals into the Mott and metallic states allows us to systematically study the evolution of the ground state under pressure. Our careful experiments have found that the prevention of a magnetic order is rather essential for the superconductivity in face-centred cubic Cs3C60, which presents a basic strategy for finding still higher T-c in this system.