jmc

Dividing by $99,$ we get $$\frac{x^2}{11}+\frac{y^2}{9^2\cdot 11}=1.$$Thus, the length of the major and minor axes are $2\sqrt{9^2\cdot 11}=18\sqrt{11}$ and $2\sqrt{11},$ respectively. Then the distance between the foci of the ellipse is $$\sqrt{(18\sqrt{11}{)}^2-(2\sqrt{11}{)}^2}=2\sqrt{11}\cdot \sqrt{9^2-1}=\boxed{8\sqrt{55}}.$$