Let \( H:\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1 , \ a>0 , \ b>0 \) be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is \( 4\left(2\sqrt{2}+\sqrt{14}\right) \). If the eccentricity \( H \) is \( \dfrac{\sqrt{11}}{2} \), then the value of \( a^2+b^2 \) is equal to __________.
