For positive real numbers $a,b,c,d$, find the remainder when the minimum possible **integer value** of the following expression is divided by $11$ $\sqrt{(a^3+b^3+c^3+d^3)\Bigl( \dfrac{2.25}{a^3}+\dfrac{20.25}{b^3} + \dfrac{42.25}{c^3}+\dfrac{400}{d^3}\Bigr)}$