Let the length of a latus rectum of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ be 10 . If its eccentricity is the minimum value of the function $f(\mathrm{t})=\mathrm{t}^2+\mathrm{t}+\frac{11}{12}, \mathrm{t} \in \mathbf{R}$, then $\mathrm{a}^2+\mathrm{b}^2$ is equal to:
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