Remember that slash chords are chords written like this: Amin7/D. When you see one, it means to play the first letter as a chord with the second letter as the bottom note in the bass.
Slash chords are often used to simplify things for the instrumentalist and they do make things simpler. If you do not label chords as slash chords, you end up labeling the bass note as the chord with a lot of 7ths, 9ths, 11ths, and 13ths.
You may have figured out that I am not a huge fan of labeling chords as slash chords. That is a preference (based on my study in jazz where slash chords are rarely used), but many great musicians disagree with me. Even many professional musicians prefer to see IV/V rather than something like V7(9)(11). So, if you want to use slash chords, feel free. However, if you like my approach better, you will still need to use slash chords in some spots. Here is an example:
This chord is clearly an A minor 7th in second inversion. It would rarely be appropriate to call it a Emin(11)(13), though that would technically be correct. (The E and G hint at E minor, the A is the 11th and the C is the 13th.)
So, if you are just dealing with an inversion, classify the chord as a slash chord. Otherwise, it is up to you whether to think of them as slash chords or not.