Urbano's conjecture on uniformly generated divisorial sheaves

Let $X$ be a projective normal variety, and let $D\in {\rm WDiv}_{\mathbb{Q}}(X)$ be a $divisor$. A divisor $A$ on $X$ is very ample if its complete linear system defines a closed embedding of $X$ into projective space.

Urbano's conjecture. There exists a very ample divisor $A$ such that $\mathcal{O}_X(mD)\otimes \mathcal{O}_X(A)^{\otimes m}$ is globally generated for every $m\geq 1$.

The conjecture asserts a uniform linear ample twist that makes all positive multiples of a rational Weil divisor globally generated. The supplied text recalls it from Urbano; no resolution is given here.