Limit, Continuity and Differentiability: JEE Main 2024 Mathematics question

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