Find ideals $I,J\subset F[x_1,x_2,\cdots x_n]$ such that $V(I)=V(J)$ but $I\neq J$

Question

Find ideals $I,J\subset F[x_1,x_2,\cdots x_n]$ such that $V(I)=V(J)$ but $I\neq J$

I understand that it is equivalent to show that $V: I\subset F[x_1,x_2,\cdots x_n]\to K^n,\, I\to V(I)$ is not one to one.

I use $I=\lbrace x^3 \rbrace$ and $J=\lbrace x^2\rbrace$ which are distict and $V(I)=V(J)=\lbrace 0 \rbrace$ Is my answer right? or I can find better examples, because it looks trivial.

Now which is the secret to find these?