Sum of two palindromes to a different base equals a third palindrome to a different base

Question

Is there a method to find when a palindrome in base $a$ plus a palindrome in base $b$ equals a palindrome in base $c$, with bases $a,b,c$ coprimes in pairs and each palindrome must have more than $2$ digits and can have a different number of terms? Example: $101$ base $11=122$ and $101$ base $13=170$ to give $122+170=292$, a palindrome in base $10$. The example illustrates that it is possible and does not put restrictions on the nature of each palindrome. Perhaps the only way to find them is by trial and error?