The corrected Cao–Dong conjecture

Let $a,b,c,l,m,n$ satisfy

$$a^l+b^m=c^n,\qquad \min\{a,b,c,l,m,n\}>1,\qquad \gcd(a,b)=1,\qquad a\equiv0\pmod{2}.$$

Corrected Cao–Dong conjecture. The equation

$$x^l+b^y=c^z$$

has only the solution $(x,y,z)=(a,m,n)$ subject to $\min\{y,z\}>1$. The survey says that this corrected conjecture has been verified in some cases but is far from solved.