Mori dream space conjecture for log canonical Fano varieties

Let $(X,\Delta)$ be a \mathbb{Q}-factorial log canonical pair such that

$$-(K_X+\Delta)$$

is ample. A Mori dream space is a projective variety with finitely generated Cox ring and the corresponding finite chamber decomposition of its effective cone.

Log canonical Fano Mori dream space conjecture. Then $X$ is a Mori dream space.

This conjecture asks for a generalisation of the known result that varieties of Fano type are Mori dream spaces. Its status is not established by the supplied text.