$\large\dfrac{\sqrt{\color{#20A900}{10}\color{#3D99F6}+\sqrt{1}}\color{#3D99F6}+\sqrt{\color{#20A900}{10}\color{#3D99F6}+\sqrt{2}}\color{#3D99F6}+\cdots\color{#3D99F6}+\sqrt{\color{#20A900}{10}\color{#3D99F6}+\sqrt{99}}}{\sqrt{\color{#20A900}{10}\color{#69047E}-\sqrt{1}}\color{#3D99F6}+\sqrt{\color{#20A900}{10}\color{#69047E}-\sqrt{2}}\color{#3D99F6}+\cdots\color{#3D99F6}+\sqrt{\color{#20A900}{10}\color{#69047E}-\sqrt{99}}}$

If the expression above equals to $a+\sqrt{b}$ for positive integers $a$ and $b$, find $a+b$.

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