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I want to know whether a/an X million growth is the same as a growth of X million.
The year 2001 witnessed a growth of 11 million in the number of households that live in a rented accommodation.
The year 2001 witnessed an 11 million growth in the number of households that live in a rented accommodation.
I want to say that a number grew by 11 million.
My personal preference would be to use "saw" and "increase", for example (a) …saw an increase of 11 million… or (b) The number of rented accommodation increased by 11 million in 2021.
If the OP wants to preserve the sense of growth, why not use it as a verb?
The year 2021 saw the number of rented accommodation grow from XXX million to XXX million.
The number of households in rented accommodation grew by 11 million in 2021
The phrase "a 11 million growth" is not idiomatic, and some might argue ungrammatical. The phrase eleven million growth begins with a vowel sound, so the indefinite article an should precede it.
E.g “An 11 million-dollar NYC apartment”
Ignoring adjectives, the slot in 'a ...... growth' is almost always filled by a scale factor expressed as a percentage, like 300%, or equivalent like threefold – not as a numeral or equivalent (300, a dozen). And 'increase' would be the more normal noun to use. But sticking with 'growth': while 'a growth of 100' is reasonably idiomatic usage, the Google ngram for 'a 100 growth' is a flatline:
Correspondingly, the ratio of Google hits in searches for and "a growth of 5000" and ["a 5000 growth" -"A ="] (the filter to avoid a major false positive) is about 140 000 : 0.
On the other hand, 'a 100% growth' outperforms 'a growth of 100%', though both are quite acceptable:
I don't like either usage, though the first is sort of grammatically correct.
Your word "witnessed" indicates some entity (person, group of people, something) that did the witnessing, and the indication that the number of renting households did the witnessing seems unlikely to be what you mean.
The phrase "witnessed an 11 million growth" is awkward; I don't know language rules that would tell you that it is awkward, unfortunately, but a native English speaker is unlikely to say that.
I agree with a comment you got that "The number ... grew by 11 million" would be simpler, clearer, easier to read, and has all the meaning you've indicated you want.
