Is solving $m^3 = k*n + c$ hard? Given the equation 
$$m^3 = k\cdot n + c$$
I know $n$ and $c$, and I need to find $k$, so that $m$ is a natural number. $n$ and $c$ are large numbers, so i can't use bruteforce. 

How can you find a solution?
Your problem is equivalent to solving $m^3 \equiv c \pmod n$. This corresponds to breaking RSA for $e=3$. We know no efficient way for doing that without factoring $n$.

If you know the factors of $n$ you can compute the private exponent $d$ as $e \cdot d \equiv 1 \pmod{\varphi(n)}$ using the extended euclidean algorithm and then compute $m$ as $c^d$.