Fingering Issues...

[leukos2013]

Hi,
Please pardon my english and musical terms/vocabulary...
I've started playing piano around last summer and it's been quite a journey. I didn't attend any class until 3 months ago and I've taught myself pretty much the basics. I would often prefer modern pieces over classical pieces. I've played a few classical pieces such as the Maiden's Prayer, and three more pieces which I've forgotten the name.
To the point...

Allegro Cantabile - Nodame Cantabile Opening (this is an anime/japanese cartoon opening song)
- This is a modern piece which I've been practicing for around 3 days. I've been practicing the part around 2:11-2:13 for quite a while now.
Link to sheets: https://josh.agarrado.net/music/anime/index.php?searchterms=allegro%20cantabile
Choose "Allegro Cantabile (Piano Version)"
On the sheets, it's located on 41st bar.
- flats are G A B D E
Right hand: A D F A D F - D (F D) F C D
Left hand:   D A D F A D - (F D) A F D A (Appregio)
According to the sheets and video, Left hand's F land with right hand's D then follows with left hand's D with right hand's F. Meaning which they land on the same notes after another... However, my left hand would often interfere with my right hand's F's landing as the left hand's F is departing for the D. I was wondering if there's any technique to prevent this kind of issue.

[leukos2013]

Right hand fingering: 5 3 1 3 5 1 - 5 2 1 2 4 3
Left hand fingering:   5 3 2 1 3 2 - 1 2 3 1 2 3