Let the length of the latus rectum of an ellipse \( \dfrac{x^{2}}{a^{2}}+\dfrac{y^{2}}{b^{2}}=1,\ (a>b), \) be \( 30 \). If its eccentricity is the maximum value of the function \( f(t)=-\dfrac{3}{4}+2t-t^{2} \), then \( \left(a^{2}+b^{2}\right) \) is equal to:
