The Andrews–Uncu conjecture for an asymmetric Rogers–Ramanujan identity

Let $(a;q)_n$ denote the $q$-Pochhammer symbol, and let $(a_1,a_2;q)_\infty=(a_1;q)_\infty(a_2;q)_\infty$. The variables $m,n$ range over nonnegative integers. The Andrews–Uncu conjecture.

$$\sum_{m,n\ge 0}\frac{(-1)^n q^{2\binom{m}{2}+9\binom{n}{2}+3mn+2m+7n}}{(q;q)_m (q^3;q^3)_n} = \frac{1}{(q^2,q^3;q^6)_\infty}.$$

This is a multiple-asymmetric Rogers–Ramanujan type identity proposed by G. E. Andrews and A. K. Uncu. The supplied source establishes a closely related identity but does not provide evidence that this conjectural identity has been resolved.