I Don't Think the a Should be There

Calculus Level 5

$\displaystyle \sum_{x=1}^{\infty} \displaystyle \log_{33}\left(\frac{(x+a-1)(x+a+1)}{(x+a-3)(x+a+3)}\right)=1$

If the sum of all possible real values of constant $$a$$ such that the infinite sum above is fulfilled can be represented as $$\frac{p}{q}$$ for coprime positive integers $$p,q$$, find $$p+q$$.

Try the harder (way harder) version here.

Try the easier version here.

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