While you could do this, the real question is whether or not you should do this.
Your resume is a statement of your qualifications, experience, and communication abilities.
If I read on a resume that you worked from May XX - July 2016, the assumption I will make is that you worked all, or a significant portion, of your final month.
This boosts your experience by a month. It is misleading.
Now, if you've worked at your previous job for several years, it probably doesn't make a big difference in your perceived level of experience. Small, but still misleading.
But if this is a short contract, say from May 2016 - June 2016, then you would be implying that you worked for 3 months instead of 2, boosting your perceived experience by 50%. Very misleading.
So, if I choose to interview you or hire you based on your resume and the truth comes out it will change how I see you as a candidate - I will see you as someone willing to mislead me for your own benefit.
I will not care that it is technically true; I will not trust you.
The alternative, is that you list May XX - June 2016 on your resume. You are now under-reporting your own experience by a day.
Will this make you look less qualified? No.
Will it effect my perception of you if I find out the truth?
Yes --> This is where you can truly convince me that you are someone worth hiring.
"So Ju-chan, you worked for company XYZ until June 2016?"
"Well, technically I worked for them until July 1st, they needed me to stay longer than my intended end date, and I really enjoyed working for them so I was happy to stay a little longer to help out" <-- this is you showing me a great example of your character as an employee.
So, you decide for yourself whether or not it's worth it.