$\large \frac{\sqrt{(\lambda +3)^2 + (\rho +3)^2 +18} + 3\lambda +3\rho +1}{\sqrt{\lambda^2 + \rho^2} +1} \geq 7$

Let $\lambda, \epsilon, \rho$ be the roots of the equation $(x+a)^3 = 0$ for real number $a$. If the inequality above is fulfilled, find the numeric value of the expression below.

$\large \frac{\sqrt{(\lambda +3)^2 + (\rho +3)^2 +18} + 3\lambda +3\rho +1}{\sqrt{\lambda^2 + \rho^2} +1}$

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