Let the domain of the function \( f(x)=\cos^{-1}\!\Big(\dfrac{4x+5}{3x-7}\Big) \) be \( [\alpha,\beta] \) and the domain of \( g(x)=\log_{2}\!\big(2-6\log_{27}(2x+5)\big) \) be \( (\gamma,\delta) \). Then \( \big|7(\alpha+\beta)+4(\gamma+\delta)\big| \) is equal to ______.
