Let \(I\left(x\right)=\int \frac{dx}{(x-11{)}^{\frac{11}{13}}(x+15{)}^{\frac{15}{13}}}.\) If \(I\left(37\right)-I\left(2…

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

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