  We extend the nuclear Density Functional Theory (DFT) by including
proton-neutron mixing and contact isospin-symmetry-breaking (ISB) terms up to
next-to-leading order (NLO). Within this formalism, we perform systematic study
of the nuclear mirror and triple displacement energies, or equivalently of the
Isobaric Multiplet Mass Equation (IMME) coefficients. By comparing results with
those obtained within the existing Green Function Monte Carlo (GFMC)
calculations, we address the fundamental question of the physical origin of the
ISB effects. This we achieve by analyzing separate contributions to IMME
coefficients coming from the electromagnetic and nuclear ISB terms. We show
that the ISB DFT and GFMC results agree reasonably well, and that they describe
experimental data with a comparable quality. Since the separate electromagnetic
and nuclear ISB contributions also agree, we conclude that the
beyond-mean-field electromagnetic effects may not play a dominant role in
describing the ISB effects in finite nuclei.
