  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 ($m_{\nu}=2$ 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.
