已知函数\(f\left( x \right)=\left| 2x+1\left| - \right|x-2 \right|\),不等式\(f\left( x \right)\leqslant 2\)的解集为\(M\).
\((1)\)求\(M\);
\((2)\)记集合\(M\)的最大元素为\(m\),若正数\(a,b,c\)满足\(abc=m\),求证:\(\sqrt{a}+\sqrt{b}+\sqrt{c}\leqslant \dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\).