Let \(\mathrm{I}\left(\mathrm{x}\right)=\int \frac{\mathrm{dx}}{(\mathrm{x}-11{)}^{\frac{11}{13}}(\mathrm{x}+15{)}^{\fra…

Let \(\mathrm{I}\left(\mathrm{x}\right)=\int \frac{\mathrm{dx}}{(\mathrm{x}-11{)}^{\frac{11}{13}}(\mathrm{x}+15{)}^{\frac{15}{13}}}.\) If \(\mathrm{I}\left(37\right)-\mathrm{I}\left(24\right)=\frac{1}{4}\left(\frac{1}{{\mathrm{b}}^{\frac{1}{13}}}-\frac{1}{{\mathrm{c}}^{\frac{1}{13}}}\right),\mathrm{b},\mathrm{c}\in \mathrm{ℕ},\) then \(3(b+c)\) is equal to

[JEE Main 2025, 23 Jan (Shift 1)]