Find the Difference!

Algebra Level 2

\(x\) is a positive real number which satisfies

\[ \sqrt {11x^2-21x+31}+\sqrt {11x^2-21x-9}=8. \]

What is the value of

\[ \sqrt {11x^2-21x+31}-\sqrt {11x^2-21x-9} ? \]

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