1. In practical organic analysis, solubility behavior is used to identify the functional group.

2. The usual diagnostic pattern for the given options is:

   • Carboxylic acids dissolve in $\mathrm{NaHCO_3}$ as well as $\mathrm{NaOH}$.
   • Phenols dissolve in $\mathrm{NaOH}$ but not in $\mathrm{NaHCO_3}$.
   • Amines dissolve in dilute $\mathrm{HCl}$.
   • Amides are generally neutral and do not show such acidic/basic solubility.

3. Now check each option:

   A: $o$-Toluidine

   • It is an amine.
   • It should dissolve in dilute $\mathrm{HCl}$ due to salt formation.
   • So this does not match a phenolic solubility profile.

   B: Benzamide

   • It is an amide.
   • It is neutral and does not characteristically dissolve in $\mathrm{NaOH}$ like a phenol.
   • So this is not the correct match.

   C: Oleic acid

   • It is a carboxylic acid.
   • It should dissolve in $\mathrm{NaHCO_3}$ and $\mathrm{NaOH}$.
   • Hence it would not fit a profile of dissolving only in strong base.

   D: $m$-Cresol

   • It is a phenol.
   • Phenols dissolve in $\mathrm{NaOH}$ but not in $\mathrm{NaHCO_3}$.
   • This matches the characteristic practical organic solubility profile.

4. Therefore, compound $X$ is $m$-Cresol.

$\boxed{\text{Option D: } m\text{-Cresol}}$

5. Comparison with stored correct answer:
   • Stored correct answer: D
   • Derived answer: D
   • They match.