Let $t$ be the area of a regular pentagon with each side equal to $1.$ Let $P\left(x\right)=0$ be the polynomial equation with least degree, having integer coefficients, satisfied by $x=t$ and the $\text{gcd}$ of all the coefficients equal to $1 .$ If $M$ is the sum of the absolute values of the coefficients of $P\left(x\right).$ What is the integer closest to $\sqrt{M}? \left[\sin 18°=\left(\frac{\sqrt{5}-1}{4}\right)\right]$