jmc

We have $(-3{)}^3=-27$, $(-4{)}^3=-64$, and $(-5{)}^3=-125$. Since $-64$ is between $-45$ and $-101$, we know that $\sqrt[3]{-64}$, which equals $\boxed{-4}$, is between $\sqrt[3]{-45}$ and $\sqrt[3]{-101}$.