Integer Indices

From this sum of powers, can you find the sum of the indices?
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Problem

Given that $5^j + 6^k + 7^l + 11^m = 2006$ where $j$, $k$, $l$ and $m$ are different non-negative integers, what is the value of $j+k+l+m$?

 

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.