Question

P=cube root of m+n divided by x+2n make n the subject

Answer 1

P= (m+n)^(1/3) / (x+2n)

or P= ( (m+n)/(x+2n) )^(1/3)
or .....

the way is sits it is too ambiguous

Answer 2

p = ∛(m+n) / (x+2n)

p^3 (x+2n)^3 = m+n
That will result in trying to solve a cubic, which gets very messy.
So, I'll go with
p = ∛((m+n)/(x+2n))
p^3 = (m+n)/(x+2n)
(x+2n)p^3 = m+n
xp^3 + 2np^3 = m+n
2np^3 - n = m - xp^3
n = (m - xp^3)/(2p^3 - 1)