If $m=u-u_{xx}$, I would like to ask if the following formula is true?

$\frac{\delta}{\delta u}=(1-\partial_{xx})\frac{\delta}{\delta m}$, where $\frac{\delta}{\delta u}$ and $\frac{\delta}{\delta m}$ are the variational derivatives;

If not, is there some other relation between $\frac{\delta}{\delta u}$ and $\frac{\delta}{\delta m}$?

Thanks.