Inverse of $(U^H X U + D)$ where U is unitary, X and D diagonal

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Given complex unitary matrix U, and full rank diagonal matrices X and D with positive entries. I'm looking for an efficient way to compute: $(U^HXU+D)^{-1}$ The matrix inversion identity doesn't really help me since all the involved matrices are full rank. If X was proportional to the identity matrix it would be problem solved :-)