  We consider cosmological models with dynamical dark energy (dDE) coupled to
cold dark matter (CDM), while simultaneously allowing neutrinos to be massive.
Using a MCMC approach, we compare these models with a wide range of
cosmological data sets. We find a strong correlation between this coupling
strength and the neutrino mass. This correlation persists when BAO data are
included in the analysis. We add then priors on $\nu$ mass from particle
experiments. The claimed detection of $\nu$ mass from the Heidelberg-Moscow
neutrinoless double--$\beta$ decay experiment would imply a 7--$8 \sigma$
detection of CDM-DE coupling. Similarly, the detection of $\nu$ mass from
coming KATRIN tritium $\beta$ decay experiment will imply a safe detection of a
coupling in the dark sector. Previous attempts to accommodate cosmic
phenomenology with such possible $\nu$ mass data made recourse to a $w < -1$
eoS. We compare such an option with the coupling option and find that the
latter allows a drastic improvement.
