\(ABC\) is an isosceles triangle with \(AC=BC\) and has an angle \(ACB=108^\circ\).

If the ratio of \(\dfrac{AB}{BC}\) can be represented as \(\dfrac{a+\sqrt{b}}{c}\), where \(a,b\) and \(c\) positive integers with \(b\) square-free, find \(a+b+c\).

**Bonus**: Try to do this without trigonometry.

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