“vor allem” versus “vor allen” — Which to use when?

Question

I'm learning German these days. I saw in a book that vor allem has the idiomatic meaning first of all. But to my confusion there is the example sentence

Die Leute liebten vor allen das gelbe Auto.

When should I use vor allem and when vor allen?

ADD

Later I saw in the grammar book :
For the pronoun all, when it refers to things, it's regarded as neutral, singular (so ..em) and when it refers to people it is regarded as plural (so ..en). (when they are after preposition I guess)

Einige sind mit allem einverstanden. (Some people agree with everything)

Wir haben vorher mit allen diskutiert. (We have discussed it with everyone before)

Answer 1

vor allem can be translated to especially, whereas vor allen can be translated into 'before everyone else' or 'in front of everyone'.

In general the word alle means all. Allem is in the third case and allem in fourth case. Allem can be used with objects and allen with people generally spoken

Answer 2

The meaning is slightly different whether you use "vor allen" or "vor allem". The following examples may help:

Er war erster, er kam vor allen anderen ins Ziel.
Das lag vor allem daran, dass er der schnellste war.

You see that in the second sentence the reason is more or less unspecific. He was the first, because of several reasons, but "vor allem", because he was the fastest. You may extend the sentence as follows:

Das lag vor allem anderen daran, dass ...
Das lag hauptsächlich daran, dass ...
Das lag vor allen Dingen daran, dass ...
Das lag vor allen anderen Dingen daran, dass ...
Das lag vor allem, was es gibt, daran, dass ...

Indeed, the comment of The_javascript_King is right. Your example is rather unusual, especially in combination with "Leute".