Probability of rolling at least one 6 in each roll when rolling multiple dice a number of times

Question

I roll $n$ fair dice $m$ times in a row. The probability to roll at least one 6 in each roll is $(1 - (5/6)^n)^m$ I think. Is that correct?

How can I find $n$ so that the probability of rolling at least one 6 in each roll is at least 95%?

Can I just say $(1 - (5/6)^n)^m > 0.95$ and solve for $n$? So that $n > \log(1 -0.95^{(1/m)})/\log(5/6)$ ?