An Inspired Number Theory problem

If the set of all pairs of positive integers $(m,n)$ that satisfy the conditions

$\gcd (m^3, n^2) = 2^2 \cdot 3^2 \text{ and } \text{lcm}(m^2, n^3) = 2^4 \cdot 3^4 \cdot 5^6?$

are $\{ (m_1, n_1) \ , \ (m_2, n_2) \ ,\ \ldots \ , \ (m_k, n_k) \}$ . If $d(x) \text{ is the no. of positive integral factors of }x$ . Then find the value of

$\large{\sum_{i=1}^k (d(m_i) + d(n_i)) = \ ? }$