The length of the diagonal can be derived from the formula: \(\sqrt {x^2 +y^2 + z^2}\).
From the given information, we can form two equations: \(4x+4y+4z=60\) and \(2xy+2yz+2zx=56\)
Simplifying the first equation, we have: \(x+y+z=15\).
Squaring the first equation, we get: \(x^2+y^2+z^2+2xy+2xz+2zy=225\)
SUbsituting what we know, we have: \(x^2+y^2+z^2 = 169\)
Now, we can take the sqaure root of this eqaution, to find that the diagonal has length \(\color{brown}\boxed{13}\)
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