Suslin's cancellation conjecture in corank one

Let $k$ be an algebraically closed field, and let $X$ be a smooth affine $k$-scheme of dimension $d\geq2$. Suslin's cancellation conjecture. If $\mathcal{E}$ and $\mathcal{E}'$ are vector bundles of corank $1$ on $X$ and

$$\mathcal{E}\oplus\mathcal{O}_X\cong\mathcal{E}'\oplus\mathcal{O}_X,$$

then $\mathcal{E}\cong\mathcal{E}'$. This asks for uniqueness in the enumeration problem for corank-one bundles, extending cancellation results in negative corank and corank zero; the supplied text does not state whether it has been resolved.