Isn't 100000 such a huge number?

Find the sum of all the values of \(x\) which satisfy the equation

\[\sqrt{x+\sqrt{100000}}=\sqrt{a}+\sqrt{b}\] where \(x, a,\) and \(b\) are positive integers.


For a related problem, see Isn't 100000 such a huge number (part 2)?

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