$(1)$计算：$\sqrt{\dfrac{1}{9}}+\sqrt[3]{\dfrac{26}{27}-1}+\left|\sqrt{3}-2\right|-2.$

$(2)$解方程组：\left\{\begin{align}&x+2y=1\\ &3x-2y=11\\\end{align}\right..

$(3)$解不等式组$\begin{cases}5(x-1)< 3x+1\\\dfrac{2x-1}{3}-\dfrac{5x+1}{2}\leqslant 1\end{cases}$，并将解集在数轴上表示出来．