The KBC void is a local underdensity with the observed relative density contrast $delta equiv 1 - rho/rho_{0} = 0.46 pm 0.06$ between 40 and 300 Mpc around the Local Group. If mass is conserved in the Universe, such a void could explain the $5.3sigma$ Hubble tension. However, the MXXL simulation shows that the KBC void causes $6.04sigma$ tension with standard cosmology ($Lambda$CDM). Combined with the Hubble tension, $Lambda$CDM is ruled out at $7.09sigma$ confidence. Consequently, the density and velocity distribution on Gpc scales suggest a long-range modification to gravity. In this context, we consider a cosmological MOND model supplemented with $11 , rm{eV}/c^{2}$ sterile neutrinos. We explain why this $ u$HDM model has a nearly standard expansion history, primordial abundances of light elements, and cosmic microwave background (CMB) anisotropies. In MOND, structure growth is self-regulated by external fields from surrounding structures. We constrain our model parameters with the KBC void density profile, the local Hubble and deceleration parameters derived jointly from supernovae at redshifts $0.023 - 0.15$, time delays in strong lensing systems, and the Local Group velocity relative to the CMB. Our best-fitting model simultaneously explains these observables at the $1.14%$ confidence level (${2.53 sigma}$ tension) if the void is embedded in a time-independent external field of ${0.055 , a_{_0}}$. Thus, we show for the first time that the KBC void can naturally resolve the Hubble tension in Milgromian dynamics. Given the many successful a priori MOND predictions on galaxy scales that are difficult to reconcile with $Lambda$CDM, Milgromian dynamics supplemented by $11 , rm{eV}/c^{2}$ sterile neutrinos may provide a more holistic explanation for astronomical observations across all scales.
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