Merriam–Webster's Dictionary of English Usage (MWDEU) has an entry for 'admit of'. It quotes Fowler (1926) pointing out "that the combination 'admit of' is more limited in application than it once was and that it usually takes a nonhuman subject" (emphasis mine).
MWDEU lists the following examples of use with a nonhuman subject:
[...] questions which, by their very nature, admit of no satifactory answer
(R. A. Posner, New Republic, 21 Aug. 2000)
They content that many words are absolutes that do not admit of comparison
The rule [...] admitted of some justification
(W. Raspberry, Springfield (Mass.) Union News, 20 Jan. 1989)
The problems of ecology [...] admit of rational solution
(A. Huxley, Center Mag., Sept. 1969)
It is a judgement that admits of no excuses
(B. Ehrenreich, N.Y. Times Book Rev., 14 Oct. 1990)
and the following example of the rare usage with a personal subject:
But even they will admit of a number of amusing eccentricities
(S. Winchester, The Professor and the Madman, 1989)
Hence, to answer the OP's question, both sentences:
The question is too general to admit one answer.
The question is too general to admit of one answer.
have essentially the same meaning. Although the latter version is rarer, it has, as Fowler points out, a nonhuman subject.