Algebra Level 4

$\frac{1}{\sqrt{1}+\sqrt{2}} + \frac{1}{\sqrt{2}+\sqrt{3}} + \frac{1}{\sqrt{3}+\sqrt{4}} +\cdots + \frac{1}{\sqrt{n}+\sqrt{n+1}}$

Find the sum of all values of $$n$$, $$1 \leq n \leq 100$$, for which the expression above is rational.

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