  We look for possible evidence of a non-minimal coupling (NMC) between dark
matter (DM) and gravity using data from the X-COP compilation of galaxy
clusters. We consider a theoretically motivated NMC that may dynamically arise
from the collective behavior of the coarse-grained DM field (e.g., via
Bose-Einstein condensation) with averaging/coherence length
$\L_{\mathrm{nmc}}$. In the Newtonian limit, the NMC modifies the Poisson
equation by a term $\L_{\mathrm{nmc}}^2 \nabla^2 \rho$ proportional to the
Laplacian of the DM density itself. We show that this term when acting as a
perturbation over the standard Navarro-Frenk-White (NFW) profile of cold DM
particles, can yield DM halo density profiles capable of correctly fitting
galaxy clusters' pressure profiles with an accuracy comparable and in some
cases even better than the standard cold DM NFW profile. We also show that the
observed relation between the non-minimal coupling length scale and the virial
mass found in Gandolfi et al., 2022 for Late Type Galaxies is consistent with
the relation we find in the current work, suggesting that the previously
determined power-law scaling law holds up to galaxy cluster mass scales.
