“Onze” is a weird word. You generally don’t elide the word that precedes it, as if it started with an aspirated h. Thus, you don’t say “*l’onze septembre” but “le onze septembre”, and you both write and pronounce:

du onze septembre

Because otherwise French would be no fun, there are of course exceptions to the “don’t elide in front of ’onze’” rule. You can (but do not have too) elide “de” and “que” in front of it. All the following sentences are correct.

Il est près d’onze heures.
Il est près de onze heures.

Nous ne serons finalement qu’onze à table ce soir.
Nous ne serons finalement que onze à table ce soir.

It is always correct not to elide the word preceding both cardinals and ordinals in French so you can take it as a rule without risk.

Le un et le deux sont sortis au loto, à la une du journal, le huit de cœur, le train de onze heures; c’est le huitième jour, la onzième de la classe, pour la énième fois.

Elided form might sometimes be observed but only to match (lazy) spoken French, :

l’huit de cœur, le train d’onze heures, l’huitième jour, l’onzième de la classe, pour l’enième fois.

but never:

L’un et le deux sont sortis au loto, à l’une du journal.

This doesn’t apply to un and une when used as an article. In the opposite the elision is mandatory in that case, eg:

L’un et l’autre. L’une ou l’autre.

This leads to both of these acceptable forms:

Une pièce d’un Euro.

Une pièce de un Euro.

There are no elisions with Onze when used in dates even in spoken French, so it is always:

du onze septembre

and never

de l’onze septembre.

Apart from numbers:

Note that de le might appear when le is a pronoun like in (thanks to Aerovistae to point it):

Il me demande de le rencontrer.

De le or de les are sometimes used for humorous purpose like in:

Le film de les Nuls.

It is also sometimes used by mistake before proper nouns while elision should be used:

La gare de Le Mans

should be

La gare du Mans, like "Les 24 heures du Mans".

Allow me to object or to complete some propositions above.

“Une pièce de un euro”, though this can be heard, is surely a fault (“d’un euro” is correct).

Besides, the precision about proper names is uncomplete. Although you can’t say :

“la gare de Le Mans”, (correct form is “la gare du Mans”)

still you must say:

“La déclaration de Le Pen” and not “La déclaration du Pen” :

The rule is that proper names with the article “Le” must be contracted in “du” for places, but not for persons.

“L’un” when “un” is a number and not an article, can effectively not be said, but you should have precised that “un”, in that case, is replaced by “as”, which is a synonym of “un” precisely made for this very case. (though most people have recently forgotten the precise meaning of “l’as”, thinking it means “the best one”: In fact, “l’as” doesn’t mean “the best one”, but precisely “the number one”, so you must say: “l’as et le deux sont sortis au loto”, and not “le un et le deux“, which is a fault, though often you can hear it.