The adjoint strict-nefness conjecture

Let $X$ be a projective manifold of dimension $n$, and let $L$ be a strictly nef divisor, meaning that $L\cdot C>0$ for every irreducible curve $C$ on $X$. Adjoint strict-nefness conjecture. Then

$$K_X+tL$$

is ample for $t>n+1$. The source places this in the context of the expectation that adjoint strictly nef divisors should be ample; it would imply that on a projective manifold with $K_X\equiv0$, strict nefness and ampleness coincide.