Find plaintext of RSA by solving extended euclidean algorith for two encrptions with two different exponents for same plaintext
If you are able to compute $m^1 \pmod{N}$, then you have (obviously) recovered the message $m$. So, you should be able to use the extended Euclidean algorithm to express $m^1 \pmod{N}$ in terms of $c_A$ and $c_B$.

Hint: It will involve exponentiations and multiplications.