  Using gauge/gravity duality as a tool, we compute the strong sector, isospin
breaking induced contribution to the neutron-proton mass difference in the
Witten-Sakai-Sugimoto model of large $N$ QCD with two non-degenerate light
flavors. The mass difference, for which we provide an analytic expression,
turns out to be positive and proportional to the down-up quark mass splitting,
consistently with expectations and previous estimates based on effective QCD
models. Extrapolating the model parameters to fit QCD hadronic observables, we
find that the strong sector contribution to the nucleon mass splitting
overcomes the electromagnetic contribution and is about $0.25\%$ of the average
nucleon mass in the model, a result which approaches recent lattice QCD
estimates. Our formula is extended to resonances and $\Delta$ baryons. We thus
use it to compute the strong sector contribution to $\Delta$ baryons mass
differences. Finally, we also provide details of how isospin breaking affects
the holographic instanton solution describing the baryons.
