GAIC Math 2024 Problem 70

The right focus $F_1$ of the ellipse $\Gamma_1: \frac{x^2}{24}+\frac{y^2}{b^2}=1 (0<b<2\sqrt{6})$ coincides with the focus of the parabola $\Gamma_2: y^2=4px(p \in Z_{+})$. The line $l$ passing through the point $F_1$ with a positive integer slope intersects the ellipse $\Gamma_1$ at points A and B, and intersects the parabola $\Gamma_2$ at points C and D. If $13|AB|=\sqrt{6}|CD|$, then $b^2+p=$ _____.