Is a set of TM deciding specific length of language reducible?
Here is a similar example, to get you started. Let $L_n$ consist of all encodings of Turing machines that accept some string of length $n$.

Claim: $L_{n-1}$ reduces to $L_n$.
Proof: Let $M$ be an input to $L_{n-1}$. Construct a new machine $M'$ which on input $x$, if $x$ starts with a zero then $M'$ rejects, and if $x=1y$ then $M'$ simulates $M$ on $y$. Then $\langle M \rangle \in L_{n-1}$ iff $\langle M' \rangle \in L_n$ (exercise).

Your proof will be different, but the proof technique will be similar.