ANSWER
[tex]f(x)+g(x)=-5x^{2/3}+5[/tex]EXPLANATION
To add two functions we have to add like terms. First let's write the functions in the sum:
[tex]f(x)+g(x)=(-7x^{2/3}-1)+(2x^{2/3}+6)[/tex]Like terms are those terms where the variable has the same exponent. In this operation we have two groups of like terms: two terms that cointain x^2/3 and two terms that contain x^0 (or in other words, where we can't see x):
[tex]f(x)+g(x)=(-7x^{2/3}+2x^{2/3})+(-1+6)[/tex]To add like terms we just have to add the coefficients:
[tex]\begin{gathered} f(x)+g(x)=(-7+2)x^{2/3}+5 \\ f(x)+g(x)=-5x^{2/3}+5 \end{gathered}[/tex]