# Triangle Complex Strike Again

Algebra Level pending

For some positive real number $$c,$$ the three complex roots of the equation $$x^3+cx+1=0$$ form a triangle of area $$\frac{3}{25}\sqrt{109}.$$ If $$c$$ can be expressed as $$\frac{a}{b}$$ for coprime positive integers $$a$$ and $$b,$$ what is $$a+b?$$

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