If P(x) is divisible by (x-1), then it can be written as (x-1)g(x), where g(x) is a polynomial of degree 3.
Letting x=1 in the equation P(x)=(x-1)g(x), we have P(1)=0, or 4-7+m+n+6=0, simplifying to m+n = -3
If P(x) leaves a remainder of 1 when divided by (x+1), then it can be written as (x+1)q(x)+30, where q(x) is a polynomial of degree 3.
Thus, letting x= -1, we have P(-1) = 30, or 4+7+m-n+6=30, simplifying to m-n = 13
We have the two systems of equations,
m+n = -3
m-n = 13.
m=5
n= -8