+26 For certain positive integers a, b, c, and d, the set of complex number z that satisfy \(|z - 5 \sqrt{3} - 5i| = 5\) is equivalent to the set of complex numbers z that satisfy \(\left| \frac{1}{z} - \frac{1}{a \sqrt{b}} + \frac{i}{c} \right| = \frac{1}{d},\) where b is not divisible by the square of a prime. Find a+b+c+d.
