The graphs of $m\left(x\right)$ and $n\left(x\right)$ are on a single rectangular plane. Here, $m\left(x\right)$ is an odd function and has a domain of all real numbers. Both $m\left(x\right)$ and $n\left(x\right)$ are one-to-one.

Find the value of $m^{-1}\left(n^{-1}\left(7\right)\right)$.