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complex output for real integral


I get complex answer for an integral from Exp[1/x^3]/x^3 over the real  

In[]:=f[n_] = Assuming[
            {Element[x, Reals], Element[n, Integers], n >= 1},
            Integrate[E^(1/x^3)/x^3, {x, n, Infinity}]

Out[]:= 1/6 (-1)^(1/3) (-3 Gamma[5/3] + 2 Gamma[2/3, -(1/n^3)])

The imaginary part of f[n] is everywhere   ~10^-16  and I could ignore 
it but I guess there is a better approach.

I'll appreciate any help.

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