Mathematics - Limits Question with Solution | TestHub

If ${\lim }_{x\to 1}\frac{(5x+1{)}^{1/3}-(x+5{)}^{1/3}}{(2x+3{)}^{1/2}-(x+4{)}^{1/2}}=\frac{\mathrm{m}\sqrt{5}}{\mathrm{n}(2\mathrm{n}{)}^{2/3}}$, where $\gcd (\mathrm{m},\mathrm{n})=1$, then $8\mathrm{m}+12\mathrm{n}$ is equal to______