# Two Two Three Three Four Four

Algebra Level 4

The complex roots of :

$(x+2)^{2}+(x+3)^{3}=(x+4)^{4}$

are $$\frac{-a\pm\sqrt{b}i}{c}$$ for positive coprime integers $$a,b,c$$.

Find $$a+b+c$$.

Details and Assumptions

$$i^2 = -1$$

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