  We consider random matrices of the form $H_N=A_N+U_N B_N U^*_N$, where $A_N$,
$B_N$ are two $N$ by $N$ deterministic Hermitian matrices and $U_N$ is a Haar
distributed random unitary matrix. We establish a universal Central Limit
Theorem for the linear eigenvalue statistics of $H_N$ on all mesoscopic scales
inside the regular bulk of the spectrum. The proof is based on studying the
characteristic function of the linear eigenvalue statistics, and consists of
two main steps: (1) generating Ward identities using the
left-translation-invariance of the Haar measure, along with a local law for the
resolvent of $H_N$ and analytic subordination properties of the free additive
convolution, allow us to derive an explicit formula for the derivative of the
characteristic function; (2) a local law for two-point product functions of
resolvents is derived using a partial randomness decomposition of the Haar
measure. We also prove the corresponding results for orthogonal conjugations.
