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Use the absolute_field method instead:
sage: L.<c> = KL.absolute_field()
sage: f = L.defining_polynomial()
sage: from_L, to_L = L.structure()
sage: to_L(b)
2/11*c^3 + 3/11*c^2 + 2/11*c - 5/11
(The output is for the choice of d = 2.)
You also get the morphism in the other direction, which can be handy:
sage: from_L(c)
b - a
(Again, the output is for the choice of d = 2.)
