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Algebra Level 5

Let $$\omega(x)=\dfrac{ax+b}{cx+d}$$, where $$a,b,c,d$$ are real numbers.

Given that: $$\omega(\omega(\omega(1)))=1$$ and $$\omega(\omega(\omega(2)))=2015$$.

Find the sum of possible values of $$\omega(1)$$.

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