Left orderable surgeries of double twist knots

A rational number $r$ is called a left orderable slope of knot $K \subset S^3$ if the 3-manifold obtained from $S^3$ by $r$-surgery along $K$ has fundamental group. In this paper we consider double twist knots $C(k, l)$ in Conway notation. For any positive integers $m$ and $n$, show that form $C(2m, -2n)$, $C(2m+1, 2n)$ or -2n)$ then there an explicit unbounded interval $I$ such $r \in I$ $K$.