The equation $x^3 - 4x^2 + 5x - \frac{19}{10} = 0$ has real roots $r,$ $s,$ and $t.$  Find the length of the long diagonal of a box with sides of length $r,$ $s,$ and $t.$The answer is in the form k\sqrt{m}+n,. Please provide the value of k + m + n.

Let's think step by step and output the final answer within \boxed{}.
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