Although very successful in explaining the observed conspiracy between the baryonic distribution and the gravitational field in spiral galaxies without resorting to dark matter (DM), the modified Newtonian dynamics (MOND) paradigm still requires DM in X-ray bright systems. Here, to get a handle on the distribution and importance of this DM, and thus on its possible form, we deconstruct the mass profiles of 26 X-ray emitting systems in MOND, with temperatures ranging from 0.5 to 9 keV. Initially we compute the MOND dynamical mass as a function of radius, then subtract the known gas mass along with a component of galaxies which includes the cD galaxy with $M/L_K=1$. Next we test the compatibility of the required DM with ordinary massive neutrinos at the experimental limit of detection ($m_{ u}=2$ eV), with density given by the Tremaine-Gunn limit. Even by considering that the neutrino density stays constant and maximal within the central 100 or 150 kpc (which is the absolute upper limit of a possible neutrino contribution there), we show that these neutrinos can never account for the required DM within this region. The natural corollary of this finding is that, whereas clusters (T $ga$ 3 keV) might have most of their mass accounted for if ordinary neutrinos have a 2 eV mass, groups (T $lsim$ 2 keV) cannot be explained by a 2 eV neutrino contribution. This means that, for instance, cluster baryonic dark matter (CBDM, Milgrom 2007) or even sterile neutrinos would present a more satisfactory solution to the problem of missing mass in MOND X-ray emitting systems.
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