Left-orderability for surgeries on twisted torus knots

We show that the fundamental group of the $3$-manifold obtained by $\frac{p}{q}$-surgery along the $(n-2)$-twisted $(3,3m+2)$-torus knot, with $n,m\ge 1$, is not left-orderable if $\frac{p}{q}\ge 2n+6m-3$ and is left-orderable if $\frac{p}{q}$ is sufficiently close to $0$.