$m=\dfrac{6n+1}{4n+2}\left(\text{ĐK}: m \ne -\dfrac{1}{2}\right)\\ m=\dfrac{25}{18}\\ \Leftrightarrow \dfrac{6n+1}{4n+2}=\dfrac{25}{18}\\ \Leftrightarrow 18(6n+1)=25(4n+2)\\ \Leftrightarrow 108n+18=100n+50\\ \Leftrightarrow 8n=32\\ \Leftrightarrow n=4(TM)$