Let \( I(x)=\displaystyle \int \frac{dx}{(x-11)^{\frac{11}{13}}(x+15)^{\frac{5}{13}}} \). If \( I(37)-I(24)=\frac{1}{4}\left(\frac{1}{b^{\frac{1}{13}}}-\frac{1}{c^{\frac{1}{13}}}\right) \), \( b,c\in \mathbb{N} \), then \( 3(b+c) \) is equal to:
\( 40 \)
\( 26 \)
\( 39 \)
\( 22 \)
