  Isospin symmetry breaking (ISB) effects in the charge radius difference
$\Delta R_{\rm ch}$ of mirror nuclei are studied using the test example of
${}^{48}$Ca and ${}^{48}$Ni. This choice allows for a transparent study of ISB
contributions since paring and deformation effects, commonly required for the
study of mirror nuclei, can be neglected in this specific pair. The connection
of $\Delta R_{\rm ch}$ with the nuclear Equation of State and the effect of ISB
on such a relation are discussed according to an Energy Density Functional
approach. We find that nuclear ISB effects may shift the estimated value for
the symmetry energy slope parameter $L$ by more than 10 MeV while Coulomb
corrections can be neglected. ISB effects on the ground-state energy and charge
radii in mirror nuclei have been recently predicted by {\it ab initio}
calculations to be relatively small, pointing to a negligible effect for the
extraction of information on the nuclear EoS. These contrasting results call
for a dedicated theoretical effort to solve this overarching problem that
impacts not only the neutron skin thickness or the difference in mass and
charge radii of mirror nuclei but also other observables such as the Isobaric
Analog State energy.
