$f_m:=x^m+x^{-m^2},m\in\mathbb{Z}$ is not a $\mathbb{Q}$ basis for $\mathbb{Q}[x,x^{-1}]$

Question

I want to show that $x$ cannot be expressed as a sum $\sum_{k\in\mathbb{Z}}q_kf_k,q_k\in\mathbb{Q}$ but I don't know how I can do this.