  Effects of the isospin-symmetry breaking (ISB) beyond mean-field Coulomb
terms are systematically studied in nuclear masses near the $N=Z$ line. The
Coulomb exchange contributions are calculated exactly. We use extended Skyrme
energy density functionals (EDFs) with proton-neutron-mixed densities, to which
we add new terms breaking the isospin symmetry. Two parameters associated with
the new terms are determined by fitting mirror and triplet displacement
energies (MDEs and TDEs) of isospin multiplets. The new EDFs reproduce MDEs for
the $T=\frac12$ doublets and $T=1$ triplets, and TDEs for the $T=1$ triplets.
Relative strengths of the obtained isospin-symmetry-breaking terms {\em are
not} consistent with the differences in the $NN$ scattering lengths, $a_{nn}$,
$a_{pp}$, and $a_{np}$. Based on low-energy experimental data, it seems thus
impossible to delineate the strong-force ISB effects from beyond-mean-field
Coulomb-energy corrections.
