Feasibility of a cryptography transformation

This is a follow-up of the question: Transformation

We are given $$g^{1/(x+m)},$$ (it is not possible to find $\frac{1}{x+m}$ due to the Discrete log problem), can we find a $k$ such that $$g^{k/(x+m)} = g^{1/(x_1+m)}\quad\text{?}$$

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are you the same user as the other bala? Would you like your accounts merged? –  Willie Wong Mar 13 '11 at 14:08
Please also read meta.math.stackexchange.com/questions/1773/… –  Willie Wong Mar 13 '11 at 14:09
As in that previous problem, are we working in the multiplicative group of integers modulo $p$, and we know $x$ and $x_1$ (and presumably also $g$)? –  Arturo Magidin Apr 12 '11 at 15:38