In the context of quantum strong coupling, the magnetic dipole (MD) emitters are largely overlooked due to the rarity of MD source and the non-magnetic nature of matters at high frequencies. Based on a semi-classic model, we theoretically demonstrate magnetic strong coupling between an MD cluster (Er³⁺: ⁴I_13/2→⁴I_15/2 transition at 1,550 nm) and an antenna-in-cavity structure. It is found that placing the plasmonic diabolo/s-diabolo nanoantenna, which supports strong electric/magnetic dipole mode, inside a dielectric cavity could largely improve the strong coupling coefficient while suppressing the cavity loss rate compared to the bare nanoantenna counterparts, empowering the magnetic quantum strong coupling at a level of 10⁴ emitters, which is remarkable considering the weak MD dipole momentum and small hotspot region at high frequency. Furthermore, the two Rabi resonance branches undergo highly asymmetrical changes upon a small variation on the environmental refractive index, which leads to an exotic exponential sensitivity profile by tracing the ratio between the two resonances widths. The proposed magnetic strong coupling for nonlinear refractive index sensing may add a new category to quantum plasmonic sensors.