  Let $A \subset \mathbb{F}_p$ of size at most $p^{3/5}$. We show $$|A+A| +
|AA| \gtrsim |A|^{6/5 + c},$$ for $c = 4/305$. Our main tools are the cartesian
product point--line incidence theorem of Stevens and de Zeeuw and the theory of
higher energies developed by the second author.
