$\left[ \overrightarrow{u};\overrightarrow{v} \right]=\left( 5m-2;-5m;-5m-1 \right)\Rightarrow \left| \left[ \overrightarrow{u};\overrightarrow{v} \right] \right|=\sqrt{{{\left( 5m-2 \right)}^{2}}+25{{m}^{2}}+{{\left( -5m-1 \right)}^{2}}}=3\sqrt{10}$ $\Leftrightarrow 75{{m}^{2}}-10m-85=0\Leftrightarrow \left[ \begin{matrix}   m=-1  \\   m=\frac{17}{15}  \\\end{matrix} \right.$.