Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{a} + \vec{b}| = 15$ and
\( \vec{a} \times (3\hat{i} - 4\hat{j} + 5\hat{k}) = (3\hat{i} - 4\hat{j} + 5\hat{k}) \times \vec{b} \)
What is the value of $|(\vec{a} + \vec{b}) \cdot (2\hat{i} + 3\hat{j} + \hat{k})|$?