We analyze the interaction of a nanomagnet (ferromagnetic) with a single photonic mode of a cavity in a fully quantum-mechanical treatment and find that exceptionally large quantum-coherent magnet-photon coupling can be achieved. Coupling terms in excess of several THz are predicted to be achievable in a spherical cavity of approximately 1 mm radius with a nanomagnet of approximately 100 nm radius and ferromagnetic resonance frequency of approximately 200 GHz. Eigenstates of the magnet-photon system correspond to entangled states of spin orientation and photon number, in which over 10{5} values of each quantum number are represented; conversely, initial (coherent) states of definite spin and photon number evolve dynamically to produce large oscillations in the microwave power (and nanomagnet spin orientation), and are characterized by exceptionally long dephasing times.