The Makar-Limanov invariant stability conjecture for polynomial extensions

Let $A$ be a commutative domain over a field of characteristic zero, and let $x_1,\dots,x_n$ be indeterminates. The Makar-Limanov invariant of a $\Bbbk$-algebra $A$ is

$$\operatorname{ML}(A)=\bigcap_{D\in\operatorname{LND}(A)}\ker(D),$$

where $\operatorname{LND}(A)$ denotes the set of locally nilpotent derivations of $A$.

Makar-Limanov invariant stability conjecture.

$$\operatorname{ML}(A[x_1,\dots,x_n])=\operatorname{ML}(A).$$

The inclusion $\operatorname{ML}(A[x_1,\dots,x_n])\subseteq\operatorname{ML}(A)$ is immediate, while the reverse inclusion is subtle and is closely connected to the cancellation problem. The supplied text gives no evidence resolving this assertion.