The minimal model conjecture in terms of Kodaira dimension

Let $X$ be a projective variety with at most terminal singularities. Minimal model conjecture. There is a minimal model $X'$ birational to $X$ if and only if

$$\kappa(X)\neq-\infty.$$

The source presents this as a strengthened formulation, notes that it is true in dimension $3$, and gives no general resolution.