The cosmetic surgery conjecture for non-trivial knots

Let $K$ be a non-trivial knot in $S^3$. For relatively prime pairs of integers $(p,q)$ and $(p',q')$ with $q,q'>0$, write $S^3_{p/q}(K)$ and $S^3_{p'/q'}(K)$ for the corresponding Dehn surgeries.

Cosmetic surgery conjecture. If $p/q\neq p'/q'$, then $S^3_{p/q}(K)$ and $S^3_{p'/q'}(K)$ are not orientation-preserving diffeomorphic.

The conjecture asserts that the unknot is the only knot in $S^3$ admitting distinct surgery slopes that produce orientation-preserving diffeomorphic three-manifolds. Its status is not resolved in the supplied source context.