We give formulae for the cumulants of complex Wishart (LUE) and inverse matrices (inverse LUE). Their large-$N$ expansions are generating functions double (strictly weakly) monotone Hurwitz numbers which count constrained factorisations in symmetric group. The two can be compared combined with a duality relation proved \[F. D. Cunden, F. Mezzadri, N. O’Connell, J. Simm, Moments random hypergeom...