\(A\backslash B=A\Rightarrow A\cap B=\varnothing\)
\(\Rightarrow\dfrac{6}{2-m}\le1-m\)
\(\Rightarrow\dfrac{6}{2-m}-\left(1-m\right)\le0\)
\(\Rightarrow\dfrac{-m^2+3m+4}{2-m}\le0\)
\(\Rightarrow\left[{}\begin{matrix}m\le-1\\2< m\le4\end{matrix}\right.\)