Seifert fibering conjecture for non-integer surgeries

Let $\kappa$ be a knot in $S^3$, and let a non-integer surgery mean surgery on $\kappa$ with a non-integral slope. A surgery is Seifert fibred when the resulting 3-manifold admits a Seifert fibration.

Seifert fibering conjecture. If non-integer surgery on $\kappa$ is Seifert fibred, then $\kappa$ is a torus knot or a cable of a torus knot.

The conjecture concerns the classification of Seifert-fibred non-integer surgeries and is stated without a resolution status in the supplied text.