If the number of ordered pairs of positive integers \((a, b)\) such that the least common multiple of \(a\) and \(b\) is \(2^5.5^{11}.11^{17}\) is \(A\), then find the sum of digits of \(A\).

**Details and Assumptions**

If the value of A is \(3456\), then you enter \(3+4+5+6 = 18 \) as your answer.

You may use a calculator.

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