Plotting a function with large negative exponents

I am trying to plot the function:

f(x)=(1-exp(-Vx^m))/(1-(1-x^m)^V)-1

for various values of $V$ and $m$ ranging from 1 to 30, and from $0leq xleq1$. How can I avoid numerical evaluation errors near zero? I’ve tried:

LogLinearPlot[(1-Exp[-4*x^6])/(1-(1-x^6)^(4))-1,{x,10^-6,1},PlotRange->{-1,1}]

But get warnings and an oscillatory behavior of the plot which I am not sure is correct, because the limit of the function is 0 at $x=0$.

f[x0_] := Limit[(1 - Exp[-4*xx^6])/(1 - (1 - xx^6)^(4)) - 1, xx -> x0]
LogLinearPlot[{f[x]}, {x, 10^-6, 1}, PlotRange -> {-.1, .1}, WorkingPrecision -> 20]