Hai đường thẳng \(d, d^{\prime}\) song song \(\Leftrightarrow\left\{\begin{array}{l}a=a^{\prime} \\ b \neq b^{\prime}\end{array} \Leftrightarrow\left\{\begin{array}{l}m^{2}=3-2 m \\ 2 m-3 \neq-1\end{array}\right.\right.\)

\(\Leftrightarrow\left\{\begin{array}{l}m^{2}+2 m-3=0 \\ m \neq 1\end{array} \Leftrightarrow\left\{\begin{array}{l}m=1 \vee m=-3 \\ m \neq 1\end{array} \Leftrightarrow m=-3\right.\right.\)

Vậy \(m=-3\) là giá trị cần tìm.