Brunella's conjecture on leaf accumulation for foliations with ample normal bundle

Let $X$ be a compact connected complex manifold of dimension $n\geq 3$, and let ${\mathscr{F}}$ be a codimension one holomorphic foliation on $X$. Suppose that the normal bundle $N{\mathscr{F}}$ is ample.

Brunella's conjecture. Every leaf of ${\mathscr{F}}$ accumulates to the singular set ${\rm Sing}({\mathscr{F}})$.

Brunella posed this question in the context of minimal sets of codimension-one holomorphic foliations. It was proved for codimension-one holomorphic foliations on a projective manifold with cyclic Picard group, but remains open in the stated generality.