  We study the impact of the mixing (LR mixing) between the standard model $W$
boson and its hypothetical, heavier right-handed parter $W_R$ on the
neutrinoless double beta decay ($0\nu\beta\beta$-decay) rate. Our study is done
in the minimal left-right symmetric model assuming type-II dominance scenario
with charge conjugation as the left-right symmetry. We then show that the
$0\nu\beta\beta$-decay rate may be dominated by the contribution proportional
to this LR mixing, which at the hadronic level induces the leading-order
contribution to the interaction between two pions and two charged leptons. The
resulting long-range pion exchange contribution can significantly enhance the
decay rate compared to previously considered short-range contributions.
Finally, we find that even if future cosmological experiments rule out the
inverted hierarchy for neutrino masses, there are still good prospects for a
positive signal in the next generation of $0\nu\beta\beta$-decay experiments.
