F visa with one week uncovered !

Hello,
I applied for a 3 months F type. For some reasons unknown to me at the Paris office they made it until 2016-04-14 but my flight back is the 2016-04-20 ! (Even tough my invitation letter from the University clearly say that I'm leaving the 20th, as does my airplane ticket reservation.)
So this is really annoying since I have to extend my entry permit for one week.
My question is, since this entry permit is a two-entry one, if I leave China for some days and then come back, will that automatically extend my entry permit for a little time ?