  We evaluate the leading-order short-range nuclear matrix element for the
neutrinoless double-beta ($0\nu\beta\beta$) decay of the nuclei most relevant
for experiments, including $^{76}$Ge, $^{100}$Mo, $^{130}$Te and $^{136}$Xe. In
our calculations, performed with the nuclear shell model and proton-neutron
quasiparticle random-phase approximation (pnQRPA) methods, we estimate the
coupling of this term by the contact charge-independence-breaking coupling of
various nuclear Hamiltonians. Our results suggest a significant impact of the
short-range matrix element, which is about $15\%-50\%$ and $30\%-80\%$ of the
standard $0\nu\beta\beta$-decay long-range matrix element for the shell model
and pnQRPA, respectively. Combining the full matrix elements with the results
from current $0\nu\beta\beta$-decay experiments we find that, if both matrix
elements carry the same sign, these searches move notably toward probing the
inverted mass ordering of neutrino masses.
