Strong coupling (SC) between two resonant plasmon modes can result in the formation of new hybrid modes exhibiting Rabi splitting with strong energy exchange at the nanoscale. However, normal Rabi splitting is often limited to $～50–320\mathrm{meV}$ due to the short lifetime of the plasmon mode. Here, we theoretically demonstrate a record Rabi splitting energy as large as 805 meV arising from the SC between the high-$Q$ plasmonic whispering gallery mode and high-$Q$ cavity plasmon resonance supported by a spherical hyperbolic metamaterial cavity, which consists of a dielectric nanosphere core wrapped in 7 alternating layers of silver/dielectric materials. In addition, the new hybrid modes formed by the SC are shown to exhibit an extralong lifetime of up to 71.9–81.6 fs, with the large electric field intensity enhancement at both the dielectric core and the dielectric layers. More importantly, the spectral ranges of SC can be tuned across an ultrabroad range from the visible to the near-IR by simply changing the dielectric core size. These findings may have potential applications in bright single-photon sources.