Gordon's Cosmetic Surgery Conjecture in the hyperbolic case

Let $\mathcal{M}$ be a $1$-cusped hyperbolic $3$-manifold. Let $\mathcal{M}(p/q)$ and $\mathcal{M}(p'/q')$ be its $p/q$- and $p'/q'$-Dehn-filled manifolds, respectively, and suppose that both are hyperbolic. Cosmetic Surgery Conjecture (Hyperbolic Case). If

$$p/q\neq p'/q',$$

then there is no orientation-preserving isometry between $\mathcal{M}(p/q)$ and $\mathcal{M}(p'/q')$. Proposed by C. Gordon in 1990, this is a well-known question about whether distinct Dehn fillings can yield the same hyperbolic manifold up to orientation-preserving isometry; it has been extensively studied, but the supplied source gives no resolution.