A strange value

Geometry Level 3

In a triangle \(\triangle ABC\), \(\overline{AC}=6\), \(\overline{AB}=9\) and \(\angle C=15°\). Then, the exact value of \(\overline{BC}\) can be expressed, in its simplest form, as \(\frac {a \sqrt {b} + a \sqrt {c}}{c}+a \sqrt {d+\sqrt {a}}\), where \(a\), \(b\), \(c\) and \(d\) are positive integers. Find \(a+b+c+d\).

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