(-5)x radicand equation 1/3x+4=-10

there is an index of 3
(-5)(1/3x+4) = 10^3
-5/3x-20=1,000
-5/3x=980
-5x=360
-x=72

ok, I will try but very confusing

-5 (assume x here means times, not x) -5[1/(3x+4)]^(1/3) = -10 ???????
or
[1/(3x+4)]^(1/3) = 2

1/(3x+4) = 8

8(3x+4) = 1

24 x + 32 = 1
24 x = -31

x = -31/24
or do you mean
-5 [(1/3)x +4 ]^(1/3) = -10
or
[(1/3)x +4 ]^(1/3) = 2 ??????
(1/3) x + 4 = 8
x/3 = 4
x = 12