We report on a search for the recently reported X(3872) state using 15.1 fb(-1) of e(+)e(-) data taken in the sqrt[s] = 9.46-11.30 GeV region. Separate searches for the production of the X(3872) in untagged gammagamma fusion and e(+)e(-) annihilation following initial state radiation are made by taking advantage of the unique angular correlation between the leptons from the decay J/psi --> l(+)l(-) in X(3872) decay to pi(+)pi(-)J/psi. No signals are observed in either case, and 90% confidence upper limits are established as (2J+1)Gamma(gammagamma)(X(3872))B(X --> pi(+)pi(-)J/psi) < 12.9 eV and Gamma(ee)(X(3872))B(X- -> pi(+)pi(-)J/psi) < 8.3 eV.