You Will Need a Square State Of Mind

Number Theory Level 3

What is the sum of the $$\displaystyle 2$$ smallest possible values of $$\displaystyle n \in \mathbb{Z}$$, such that both $$\displaystyle 2n+1$$ and $$\displaystyle 3n+1$$ are perfect squares?

Bonus Find the GCD of all such $$n$$.

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