Least zero of pairs of additive cubic equations

An effective upper bound is established for the least non-trivial integer solution to the system of cubic forms $$\{\begin{array}{l}F=c_1{x}_1^3+c_2{x}_2^3+\cdots +c_n{x}_n^3=0,\\ G=d_1{x}_1^3+d_2{x}_2^3+\cdots +d_n{x}_n^3=0,\end{array}$$ under the “$M$-good” condition for $n\ge 16$, where $c_1,\dots ,c_n$ and $d_1,\dots ,d_n$ are integers. Additionally, a range is derived for the probability that randomly selected simultaneous equations satisfy the $M$-good condition.