Newell-type plethysm equality

Let $m,n$ be positive integers, let $\nu$ be a partition of $n$, and let $\nu'$ denote its conjugate partition. For a partition $\tau$ of $mn$, write $p^{\tau}_{\nu,(m)}$ for the corresponding plethysm coefficient. Newell-type conjecture. If $\lambda\vdash mn$, then

$$p^\lambda_{\nu,(m)}=p^{\lambda+(1^n)}_{\nu',(m+1)}$$

for any $\nu\vdash n$. This is presented as a generalization of Newell's result. The source provides no resolution, so the equality remains open in the stated generality.