Conservation of momentum require
$m_1 \vec{v_1}+m_2\vec{v_2}=m_1 \vec{v_1}'+m_2\vec{v_2}'$
If $m_1=m_2$, it reduced to
$\vec{v_1}+\vec{v_2}= \vec{v_1}'+\vec{v_2}'$

Velocity is a vector which is not the same a speed!
You can check that the sum of x (or y) component of velocity should be the same before and after collision (when $m_1=m_2$)